Mathematics for Elementary Teachers with Activities, Books a la carte edition (5th Edition)
5th Edition
ISBN: 9780134423319
Author: Sybilla Beckmann
Publisher: PEARSON
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Chapter 15.1, Problem 11P
The following problem is an example of the capture—recapturemethod of population estimation. A researcher wants to estimate the number of rabbits in a region. The researcher sets some traps and catches 30 rabbits. After the rabbits are tagged, they are released unharmed. A few days later the researcher sets some traps again and this time catches 35 rabbits. Of the 35 rabbits trapped, 5 are tagged, which indicates that they had been trapped a few days earlier. Based on these results, what is the best estimate you can give for the number of rabbits in the region? Solve this problem in three different ways, explaining your reasoning in each case.
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Pidgeonhole Principle
1. The floor of x, written [x], also called the integral part, integer part, or greatest integer, is defined
as the greatest integer less than or equal to x. Similarly the ceiling of x, written [x], is the smallest
integer greater than or equal to x. Try figuring out the answers to the following:
(a) [2.1]
(b) [2]
(c) [2.9]
(d) [2.1]
(e) [2]
(f) [2.9]
2. The simple pidgeonhole principle states that, if you have N places and k items (k> N), then at
least one hole must have more than one item in it. We tried this with chairs and students: Assume you
have N = 12 chairs and k = 18 students. Then at least one chair must have more than one student on
it.
3. The general pidgeonhole principle states that, if you have N places and k items, then at least one
hole must have [] items or more in it. Try this out with
(a) n = 10 chairs and k = 15 students
(b) n = 10 chairs and k = 23 students
(c) n = 10 chairs and k = 20 students
4. There are 34 problems on these pages, and we…
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
Q2.2
1 Point
Determine if the set of vectors spans R³.
they span R³
they do not span R³
Save Answer
23
Q2.3
1 Point
Determine if the set of vectors is linearly independent or linearly dependent.
linearly independent
O linearly dependent
Save Answer
1111
1110
Q2.4
1 Point
Determine if the set of vectors spans R4.
O they span R4
they do not span IR4
1000;
111O'
The everything combined problem
Suppose that a computer science laboratory has 15 workstations and 10 servers. A cable can be used to
directly connect a workstation to a server. For each server, only one direct connection to that server can be
active at any time.
1. How many cables would you need to connect each station to each server?
2. How many stations can be used at one time?
3. How many stations can not be used at any one time?
4. How many ways are there to pick 10 stations out of 15?
5. (This one is tricky) We want to guarantee that at any time any set of 10 or fewer workstations can
simultaneously access different servers via direct connections. What is the minimum number of direct
connections needed to achieve this goal?
Chapter 15 Solutions
Mathematics for Elementary Teachers with Activities, Books a la carte edition (5th Edition)
Ch. 15.1 - Give two examples of a statistical question and...Ch. 15.1 - A class has a collection of 100 bottle caps and...Ch. 15.1 - Neil, a third-grader, asked 10 of his classmates...Ch. 15.1 - An announcer of a TV program invited viewers to...Ch. 15.1 - There is a bowl containing 300 plastic tiles. Some...Ch. 15.1 - There is a bowl containing 80 green tiles and an...Ch. 15.1 - At a factory that produces doorknobs, 1500...Ch. 15.1 - At a factory that produces switches, 3000 switches...Ch. 15.1 - At a light bulb factory, 1728 light bulbs are...Ch. 15.1 - Carter has a large collection of marbles. He knows...
Ch. 15.1 - The following problem is an example of the...Ch. 15.1 - A group studying violence wants to determine the...Ch. 15.2 - Three third-grade classes are having a contest to...Ch. 15.2 - Find 3 coins of any type (as long as all 3 have a...Ch. 15.2 - Table 15.3 shows women’s 400-meter freestyle...Ch. 15.2 - Using an Internet browser, go to census.gov, the...Ch. 15.2 - Using an Internet browser, go to the webpage of...Ch. 15.2 - Using an Internet browser, go to one of the...Ch. 15.2 - Using an Internet browser, go to one of the...Ch. 15.2 - a. Describe in detail an activity suitable for use...Ch. 15.3 - In your own words, explain why the following two...Ch. 15.3 - Explain why the mean of a list of numbers must...Ch. 15.3 - Explain why the mean of two numbers is exactly...Ch. 15.3 - Shante caught 17 ladybugs every day for 4 days....Ch. 15.3 - John’s average annual income over a 4-year period...Ch. 15.3 - Tracy’s times swimming 200 yards were as follows:...Ch. 15.3 - Explain how you can quickly calculate the mean of...Ch. 15.3 - Explain how you can quickly calculate the mean of...Ch. 15.3 - average on her first 3 math tests was 80. Her...Ch. 15.3 - A teacher gives a 10-point test to a class of 10...Ch. 15.3 - In your own words, describe how to view the mean...Ch. 15.3 - Discuss Jessica’s reasoning about calculating the...Ch. 15.3 - ]The dot plot in Figure 15.21 represents the...Ch. 15.3 - For each of the following situations, decide...Ch. 15.3 - A teacher gives a 10-point test to a class of 9...Ch. 15.3 - A teacher gives a 10-point test to a class of 9...Ch. 15.3 - In Ritzy County, the average annual household...Ch. 15.3 - In county A, the average score on the grade 5 Iowa...Ch. 15.3 - a. The histogram at the top of Figure 15.22 shows...Ch. 15.3 - * Ms. Smith needs to figure her students’ homework...Ch. 15.3 - The average speed of a moving object during a...Ch. 15.4 - What is the difference between scoring in the 90th...Ch. 15.4 - What is the purpose of reporting a student’s...Ch. 15.4 - The three histograms in Figure 15.37 show the...Ch. 15.4 - At a math center in a class, there is a bag filled...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Refer to the...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Refer to the...Ch. 15.4 - Refer to Figure 15.26 on page 706. a. Write at...Ch. 15.4 - Use the NAEP long-term trend data about...Ch. 15.4 - Determine the median and interquartile range for...Ch. 15.4 - a. Make a box plot for the data in Figure 15.38....Ch. 15.4 - Determine the medians and interquartile ranges for...Ch. 15.4 - a. Make box plots for the dot plots in Figure...Ch. 15.4 - A fifth-grade class is wondering ¡f girls’ names...Ch. 15.4 - Compute the mean and the MAD for each of the dot...Ch. 15.4 - On a state-wide test graded on a 10-point scale,...Ch. 15.4 - A 400-point test is given to a group of students....
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